KDEMultivariate.imse()

KDEMultivariate.imse(bw) [source]

Returns the Integrated Mean Square Error for the unconditional KDE.

Parameters:

Parameters:	bw: array_like : The bandwidth parameter(s).
Returns:	CV: float : The cross-validation objective function.

bw: array_like :

The bandwidth parameter(s).

Returns:

CV: float :

The cross-validation objective function.

See p. 27 in [R6] for details on how to handle the multivariate estimation with mixed data types see p.6 in [R7].

The formula for the cross-validation objective function is:

$CV=\frac{1}{n^{2}}\sum_{i=1}^{n}\sum_{j=1}^{N}\bar{K}_{h}(X_{i},X_{j})-\frac{2}{n(n-1)}\sum_{i=1}^{n}\sum_{j=1,j\neq i}^{N}K_{h}(X_{i},X_{j})$

Where $\bar{K}_{h}$ is the multivariate product convolution kernel (consult [R7] for mixed data types).

[R6]	(1, 2) Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007)

[R7]	(1, 2, 3) Racine, J., Li, Q. ?Nonparametric Estimation of Distributions with Categorical and Continuous Data.? Working Paper. (2000)

Links:

doc_statsmodels

2017-01-18 16:11:14

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